Distributions of the Two-Dimensional DCT Coefficients for Images

For a two-dimensional discrete cosine transform (DCT) image coding system, there have been different assumptions concerning the distributions of the transform coefficients. This paper presents results of distribution tests that indicate that for many images the statistics of the coefficients are best approximated by a Gaussian distribution for the DC coefficient and a Laplacian distribution for the other coefficients. Furthermore, from a simulation of the DCT coding System it is shown that the assumption that the coefficients are Laplacian yields a higher actual output signal-to-noise ratio and a much better agreement between theory and simulation than the Gaussian assumption.